A force acts on a $3 \,gm$ particle in such a way that the position of the particle as a function of time is given by $x = 3t - 4{t^2} + {t^3}$, where $x$ is in metres and $t$ is in seconds. The work done during the first $4 \,seconds$ is ..... $mJ$
A force acts on a $3 \,gm$ particle in such a way that the position of the particle as a function of time is given by $x = 3t - 4{t^2} + {t^3}$, where $x$ is in metres and $t$ is in seconds. The work done during the first $4 \,seconds$ is ..... $mJ$
$530$
$450$
$490$
$576$
A force acts on a $3 \,gm$ particle in such a way that the position of the particle as a function of time is given by $x = 3t - 4{t^2} + {t^3}$, where $x$ is in metres and $t$ is in seconds. The work done during the first $4 \,seconds$ is ..... $mJ$
$W=\frac{1}{2} m\left(v_4^2-v_0^2\right)$
$v=\frac{d x}{d t}=3-8 t+3 t^2$
$\therefore V_0=3 m / s$ and $v_4=19 m / s$
$\therefore W=\frac{1}{2} \times 0.03 \times\left(19^2-3^2\right)=5.28\; J$
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